mathslover
  • mathslover
Prove that if the 3 altitudes of a triangle are equal then the triangle is equilateral. See attachment
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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mathslover
  • mathslover
I tried to do this and have got so far that AB = AC
1 Attachment
mathslover
  • mathslover
@ParthKohli
mathslover
  • mathslover
@experimentX

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mathslover
  • mathslover
I took following triangles :ABF and AEC by AAS I got both of these triangles congruent and therefore by CPCT AB = AC
mathslover
  • mathslover
(CPCT = Congruent Parts of Congruent Triangles are equal)
anonymous
  • anonymous
That idea should work to get that AB=BC as well.
mathslover
  • mathslover
So far , we have got ABC as isosceles. Now, I took triangle ABC and AFC both of these triangles are congruent by RHS BF = FC ( by CPCT ) therefore F is mid point of BC an AF is median and altitude also Therefore , this is the property of an equilateral triangle , so ABC is an equi. triangle
mathslover
  • mathslover
Is this correct?
mathslover
  • mathslover
You mean to take ABE and BEC triangles @joemath314159 ?
anonymous
  • anonymous
yep. and do exactly what you did with the other triangles again.
mathslover
  • mathslover
I meant this : ADC and ABD in the above comment.
mathslover
  • mathslover
OK wait..
mathslover
  • mathslover
I think I had tried that earlier but I didnt' get any favorable result , wait let me do it again
anonymous
  • anonymous
there are many combinations you could take. The pair I see is triangles BEC and BDA.
mathslover
  • mathslover
Oh yes that will work ... BEC and BDA .. this gives some output to me.
mathslover
  • mathslover
Thanks a lot @joemath314159 for your help .. Might gonna work in more concentration for me..

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